Glass fragments reassembling themselves by chance

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HonoreDB
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Glass fragments reassembling themselves by chance

Postby HonoreDB » Tue Mar 29, 2011 12:46 am UTC

I knock a glass off a table. It falls, and shatters into a specific arrangement of fragments, each of which contains a specific amount of heat energy in a specific configuration, and so on. While the fact that it would shatter was predictable in advance, if we describe the exact outcome specifically enough it becomes very unlikely. Call this very specific outcome "event one."

I gather up the fragments and sweep them off the same table at the same height. As they land, they reassemble themselves, purely by chance, back into an identical glass. Call this highly surprising outcome "event two."

Which event is more probable?

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Re: Glass fragments reassembling themselves by chance

Postby Dopefish » Tue Mar 29, 2011 1:24 am UTC

Surely theres infinitely many possible configurations for the (whole glass/fragments of glass) to fall into, and thus both would have probability 0, and thus would be equally probable.

Although things are kindve wierd when dealing with infinity and probability at once, since probability 0 != "could never happen", so I'm not sure if theres differing degrees of probability 0. I think in this case they'd be the same degree (if multiple degrees even do exist) though and thus they have equal probabilties of occuring, specifically, 0.

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Charlie!
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Re: Glass fragments reassembling themselves by chance

Postby Charlie! » Tue Mar 29, 2011 1:39 am UTC

One, because of the requirement that the shards be swept off the table. I think that coming from a broken glass makes shards less likely than average to all move in the same direction, and so by time reversal symmetry all falling in the same direction is less likely to correspond to a glass.
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Re: Glass fragments reassembling themselves by chance

Postby BlackSails » Tue Mar 29, 2011 3:00 am UTC

Its probably roughly the same probability, since each outcome is a single point in phase space.

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Re: Glass fragments reassembling themselves by chance

Postby big boss » Tue Mar 29, 2011 3:44 am UTC

couldn't you employ an entropy argument? Since entropy always increases and outcome one has more entropy (it is more disordered), therefore outcome 1 is more likely than the ordered state of outcome 2.
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Re: Glass fragments reassembling themselves by chance

Postby iChef » Tue Mar 29, 2011 5:24 am UTC

Wouldn't one be much more likely than a completely random shattering due to scratches on the glass, flaws in in from when it was made, the height at which it was dropped. When tending bar I've seen nearly identical (coming from the same factory, used and stored in the same manner) glasses break in a nearly identical pattern (around the middle with a split up the side due to how they were stacked which causes stress on the center of the glass). While it is highly unlikely that the exact same break happens it is still far, far more likely than having the glass re-assemble (which my boss would love, my glassware broker, not so much).
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BlackSails
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Re: Glass fragments reassembling themselves by chance

Postby BlackSails » Tue Mar 29, 2011 5:48 am UTC

big boss wrote:couldn't you employ an entropy argument? Since entropy always increases and outcome one has more entropy (it is more disordered), therefore outcome 1 is more likely than the ordered state of outcome 2.


You cant use an entropy argument, since we are singling out a single microstate. Thermodynamics is for ensembles.

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Re: Glass fragments reassembling themselves by chance

Postby JWalker » Tue Mar 29, 2011 6:42 am UTC

Event one is more probable than event two. Event two is classically impossible as the shattering of the glass distorts the resulting shards such that even if you put them back together by hand you wont be able to reassemble the glass. The pieces will not fit together correctly.

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Re: Glass fragments reassembling themselves by chance

Postby Little Richie » Wed Mar 30, 2011 4:53 am UTC

JWalker wrote:Event half-two is more probable than event three. Event three is classically impossible as the shattering of the glass distorts the resulting shards such that even if you put them back together by hand you wont be able to reassemble the glass. The pieces will not fit together correctly.


In this argument wouldn't these changes you are describing be reversed in event three by the same forces that caused them in half-two? When you are reassembling the glass by hand, you are not bringing the extra energy of the fall into the system.
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Re: Glass fragments reassembling themselves by chance

Postby Zamfir » Wed Mar 30, 2011 8:35 am UTC

JWalker wrote:Event half-two is more probable than event three. Event three is classically impossible as the shattering of the glass distorts the resulting shards such that even if you put them back together by hand you wont be able to reassemble the glass. The pieces will not fit together correctly.

Nah, it's purely an statistical effect that the local distortions tend not to match up. The odds of ending up distorted into a single particular non-fitting configuration are farily comparable to the odds of being distorted back to a fitting configuration. There are just many more non-fitting configurations than fitting ones.

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Re: Glass fragments reassembling themselves by chance

Postby Technical Ben » Wed Mar 30, 2011 2:57 pm UTC

I still go by the statistics of observation... I've never observed a glass reassembling. ;)
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Re: Glass fragments reassembling themselves by chance

Postby Glass Fractal » Wed Mar 30, 2011 3:36 pm UTC

Technical Ben wrote:I still go by the statistics of observation... I've never observed a glass reassembling. ;(

This would be my response, too. Glass can't reassemble just from two pieces bumping into each other.

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Re: Glass fragments reassembling themselves by chance

Postby gmalivuk » Wed Mar 30, 2011 3:56 pm UTC

Technical Ben wrote:I still go by the statistics of observation... I've never observed a glass reassembling. ;(
You've never observed a glass shattering in *exactly* the same way twice, either. Thus, as already stated, both events are of comparable likelihood.
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Re: Glass fragments reassembling themselves by chance

Postby sikyon » Wed Mar 30, 2011 8:54 pm UTC

Comparable. I would even go so far as to say that event 3 is more likely, given that a whole glass is at a more energetically favorable state than a shattered glass (less surface energy).

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Bonooru1234
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Re: Glass fragments reassembling themselves by chance

Postby Bonooru1234 » Sun Apr 03, 2011 4:36 am UTC

event one is more likely, eventually you will predict where the glass shards will land.
but when a glass breaks the top pieces land with the bottom pieces, this means that they will be at the same level when they fall and they will hit the ground at the same time, this means that it is impossible for the glass to reform because for it to do that would require the top to fall slower than the bottom

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Re: Glass fragments reassembling themselves by chance

Postby Technical Ben » Sun Apr 03, 2011 8:04 am UTC

gmalivuk wrote:
Technical Ben wrote:I still go by the statistics of observation... I've never observed a glass reassembling. ;(
You've never observed a glass shattering in *exactly* the same way twice, either. Thus, as already stated, both events are of comparable likelihood.

Huh. I'm happy with no 2 events being the same. How does that show event 3 is more likely?

[edit]
In a mathematical model, where we only include atomic positions, and ignore everything from gravity to air friction, then yes, every position of atoms is as likely as the other. But a "glass" falling off a "table" make me think 100% in real world terms. In which case, there are more forces working against the glass coming together, than it falling apart.

[double edit]
I think my main confusion has been down to the cheese graters and the numbers being swapped. Sorry. :oops:
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Re: Glass fragments reassembling themselves by chance

Postby Seli » Sun Apr 03, 2011 3:23 pm UTC

Atoms in bulk glass are distributed differently from the atoms in the surface layer, on breaking the glass the atoms at the new surfaces are re-distributed. This would have to be reversed in spontaneous reassembly, which probably makes spontaneous re-assembly orders of magnitude more unlikely than any specific breakage pathway. Entropy for the win.

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Re: Glass fragments reassembling themselves by chance

Postby Charlie! » Sun Apr 03, 2011 10:19 pm UTC

The fact that you said "entropy" should be a red flag that the problem probably accounts for that.
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